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Part of 2008 Bundeswettbewerb Mathematik

Problems(2)

How many matches compose the parallelogram's perimeter?

Source: Germany Bundeswettbewerb Mathematik 2008, Round 1, Problem 1

Fedja used matches to put down the equally long sides of a parallelogram whose vertices are not on a common line. He figures out that exactly 7 or 9 matches, respectively, fit into the diagonals. How many matches compose the parallelogram's perimeter?

geometryperimeterparallelogramtrigonometrycombinatorics unsolvedcombinatorics

Bundeswettbewerb Mathematik 2008 equation

Source: Germany Bundeswettbewerb Mathematik 2008, Round 2, Problem 1

Determine all real

x

satisfying the equation \sqrt[5]{x^3 \plus{} 2x} \equal{} \sqrt[3]{x^5\minus{}2x}. Odd roots for negative radicands shall be included in the discussion.

inequalitiesalgebra unsolvedalgebra